The microcirculation is a dynamic structure. Networks of microvessels are generated and modified during many physiological and pathological processes, including development, growth, exercise, estrus cycle, collateral formation following ischemia, wound healing and tumor growth, and in tissue engineering. The main processes determining vascular structure after initial development are angiogenesis and structural adaptation. The primary function of the circulatory system is mass transport, and oxygen is the most critical metabolite transported. Oxygen delivery to tissue depends on the vascular network structure and on the distribution of red blood cell flux, which is influenced by the mechanical behavior of red blood cells. This project addresses the following question: How do the processes of angiogenesis and structural adaptation generate vascular structures and blood flows that meet the oxygen needs of the tissue? Theoretical models will be used to analyze the interacting biological processes and physical phenomena involved in structural adaptation and blood flow. The models will be based on and tested using experimental data from the Consultants. Specific Aim 1 is to develop theoretical models for the growth and regression of microvascular networks. The models will use a segment-based approach to describe vascular network structure, combined with a continuous field description of oxygen and growth factor diffusion. The model will be (a) applied to fully three-dimensional problems, including networks in muscle; (b) extended to include splitting as well as sprouting angiogenesis (intussusceptions). Hypotheses: (i) The processes of stochastic angiogenesis, structural adaptation and pruning can generate networks that combine hierarchical tree-like structures for efficient convective transport over large distances, dense space-filling meshes for short diffusion distances to every point in the tissue. (ii) Splitting angiogenesis occurs when stimuli for angiogenesis and for diameter increase coincide. Specific Aim 2 is to develop theoretical models for blood flow in microvessels and bifurcations, including effects of the endothelial surface layer. A computationally efficient method will be used for simulating the motion and deformation of multiple interacting red blood cells. The model will be used (a) to examine the effects of interactions between red blood cells and walls on their migration away from the wall, including effects of endothelial surface layer glycocalyx); (b) to examine the motion of multiple interacting cells in diverging microvessel bifurcations, including effects of endothelial surface layer. Hypotheses: (i) The width of the cell-free layer is determined by the combined effects of red blood cell interactions with each other and with the endothelial surface layer, and can be predicted by a model including these effects. (ii) The partition of hematocrit in diverging bifurcations can be predicted based on the upstream distribution of cells and the effects of cell-cell interactions.